Pairwise f-mutual information matrices are positive semi-definite for all finite-alphabet distributions exactly when the f generator has a power series with all nonnegative coefficients that converges on the positive reals.
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A Global Characterization of $f$-Divergences Yielding PSD Mutual-Information Matrices
Pairwise f-mutual information matrices are positive semi-definite for all finite-alphabet distributions exactly when the f generator has a power series with all nonnegative coefficients that converges on the positive reals.